Expected Value: The One Number Every Casino Game Boils Down To

Expected Value, In Plain Terms

If there's a single concept worth carrying away from all of this, it's expected value (EV) — the average amount you'd win or lose per bet if you repeated it a huge number of times. It squashes every possible outcome down into one honest, unglamorous figure.

The formula: EV = Σ (Outcome × Probability)

Looks dry written out like that. In practice, it's arguably the sharpest lens available for thinking about any decision involving uncertainty.

A Simple Warm-Up Example

Imagine a mate offers you a coin flip: heads, you win £2; tails, you lose £1.

EV = (0.5 × £2) + (0.5 × –£1) = £1.00 – £0.50 = +£0.50

You'd take that deal every single time — it's worth 50p to you on average, per flip. Casino games, unfortunately for us, are essentially never built this way round. The player's EV is almost always negative. That's the entire business model.

EV Applied to Roulette

A £1 straight-up bet on European roulette:

• Win outcome: 35 × (1/37) = £0.9459
• Lose outcome: –1 × (36/37) = –£0.9730
• EV = –£0.027 per bet

Two and a half pence doesn't sound like anything. But stake £1, a thousand times, and you're down £27 in expectation. Do the same at £10 a spin and it becomes £270. Small percentages, big totals once you multiply. Our roulette maths breakdown covers the full workings.

Two Ways to Spend a Fiver Note — Sorry, a Hundred

Say you've earmarked £100 for a night's entertainment. Here's what EV reveals about two different plans:

Option A — 200 spins on a 96% RTP slot at £0.50 a spin:

• Total wagered: £100
• EV: £100 × –0.04 = –£4.00
• Expected finishing balance: roughly £96

Option B — 50 hands of blackjack at £2 a hand, playing basic strategy:

• Total wagered: £100
• EV: £100 × –0.005 = –£0.50
• Expected finishing balance: roughly £99.50

Same £100, an eightfold difference in mathematical cost. Whether the slot's more entertaining for you is your call — but the numbers themselves aren't close. Our house edge guide explains exactly why this gap exists.

Why a Single Session Tells You Nothing

This is where things trip people up constantly. "I walked away £200 up on the slots last weekend!" Lovely — genuinely. But one night's result says nothing about the game's underlying maths. You could just as easily win £200 one evening and drop £300 across the next three.

EV isn't a forecast for any one session — it's the direction things drift toward over time. Given enough repetitions, your actual results converge on that expected figure, a phenomenon known as the Law of Large Numbers, which gets its own dedicated article.

Comparing Wildly Different Bets, Fairly

One of EV's great strengths is letting you compare completely unrelated games on equal terms:

A £1 blackjack bet, mathematically, costs roughly a fifth of what a £1 slot spin does. That's not a verdict on which is "better" — that depends what you're actually after — but at least the choice is made with your eyes open.

The Jackpot Illusion

This is where thinking in EV genuinely earns its keep. A progressive slot might flash up a £3 million headline prize. Thrilling, no argument. But if that spin's actual EV works out to –£0.08, you're paying considerably more per bet than most table games ask for. The jackpot exists, sure, but your odds of ever touching it are vanishingly small.

That eye-catching number on the screen is doing some serious psychological anchoring — a topic we explore further in our piece on slot volatility. EV strips away the spectacle and shows you what you're really paying.

Expected value doesn't predict what will happen on any given spin. It tells you what the maths says should happen, averaged out. That's about as honest a framework as exists for weighing up any bet.

It's Not Just a Casino Thing

EV thinking shows up well beyond the casino floor — insurers, investors, and poker players all lean on it constantly. Once it clicks, you've got a genuinely versatile tool for any decision involving uncertainty. And the same cognitive biases that warp gambling decisions turn up in money and life choices too.